Problem: A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit.  Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red.  The deck is randomly arranged. What is the probability that the top card is red and the second card is black?
Explanation: There are 26 ways to choose the first card to be red, then 26 ways to choose the second card to be black.  There are $52 \times 51$ ways to choose any two cards.  So the probability is $\dfrac{26 \times 26}{52 \times 51} = \boxed{\dfrac{13}{51}}$.